By understanding a few basic physics principles, you can manipulate and exploit the natural resonant frequencies of your guitar and get some truly amazing sounds.
The Theory
Everything in nature has one or more resonant frequencies. These frequencies are a property of that object, and are determined by a number of factors, including density, size, shape, material, internal structure, etc. The reason this matters is that if you disturb an object with a force that has the same frequency as one of the object's resonant frequencies, the object starts going crazy. An famous example is hitting the E key on a piano and seeing the E string on a nearby guitar start to resonate. What happens is the sound waves moving through the air at a frequency for the note E hit the E string on the guitar. Well, a resonant frequency of that string is E (that's why it's called an E string). So you get a very efficient transfer of energy from the source (the piano key and then the resulting sound wave) to the object (the string).
This doesn't just apply to musical instruments, however. If you look at pictures of the aftermath of earthquakes in big cities, you can see completely destroyed buildings right next to buildings that look brand new. The reason this happens is because the resonant frequency of the destroyed building was very close to the frequency of vibrations produced by the earthquake. For that reason there was a very efficient transfer of energy between earthquake and building, and the building shakes and shakes until it tears itself apart. On the other hand, the surviving building has a resonant frequency very different from the earthquake. For this reason, the transfer of energy was very inefficient and the earthquake couldn't do that much to the building.
Well, that's all fine and good, but how does it help my guitar-playing skills?
Guitars, like many musical instruments, are designed to have lots and lots of natural resonant frequencies. This abundance of resonances means that you'll get a strong, clear sound no matter what note you play. The guitar can be split up into two sections: the body (main cavity + neck) and the strings. Each of these sections have natural frequencies that help make the guitar sound better. While you can't do much with the way the body of your guitar is set up, you can adjust the resonant frequencies of your strings. That's what tuning is. When you turn the tuning knobs, you're adjusting the tension in the string. When the tension goes up, the resonant frequency of the string goes up, giving the string a higher pitch. Conversely, when the tension goes down, the resonant frequency of the string goes down, giving the string a lower pitch.
What this means for you is that you add very complex harmonies to simple melodies without actually playing any of the harmonics. The simplest way to do this is to start with the guitar in standard tuning. Figure out a simple melody that you can play using only the top two strings. Once you've done this, tune the lower four strings of the guitar to various frequencies that "fit" the melody; i.e. they appear in the chord structure of the song. Make sure to choose both major-sounding pitches like thirds or fifths and less structured pitches as they fit into the chord structure. Play the melody slowly, giving plenty of time for each individual note to resonate. Make sure that you do not touch the other strings. As you play, the four lower strings will resonate and make chords that complement the melody. As you move into different sections of the melody, the "ghost chords" will change to match it. Try out a number of different configurations to see which one produces the sound you like best.
This is especially fun for people who know advanced music theory, since they will be able to create a number of different, interesting sounds based on the chord structures of a song. But anyone able to play a simple melody on a guitar should be able to get hours of fascinating and rewarding music out of this.